A unified framework for M-estimation based robust Kalman smoothing

We consider the robust smoothing problem for a state-space model with outliers in measurements. A unified framework for robust smoothing based on M-estimation is developed, in which the robust smoothing problem is formulated by replacing the quadratic loss for measurement fitting in the conventional Kalman smoother by a robust cost function from robust statistics. The majorization-minimization method is employed to iteratively solve the formulated robust smoothing problem. In each iteration, a surrogate function is constructed for the robust cost, which enables the states update procedure to be implemented in a similar way as that in a conventional Kalman smoother with a reweighted measurement covariance. Numerical experiments show that the proposed robust approach outperforms the traditional Kalman smoother and several robust filtering methods.